This week, her remarkable quest made headlines, as thousands of strangers from around the world – from India, Indonesia, America and Sri Lanka – offered to be tested to see if they are suitable donors. It was an extraordinary show of altruism in response to a daughter’s desperation and a mother’s desire to live.

Though Stephanie’s childhood was characterised by happy memories – of sun-drenched days at the beach, boisterous Christmas lunches and family trips to London – it was cut abruptly short when she was 11. “That’s when my mum was diagnosed with a rare kidney disorder,” says Stephanie. “Normal life changed overnight.

“Suddenly, our daily existence became all about trips to the hospital, tests and charts. Mum was put on steroids and became really sick, then she had terrible mood swings and depression. I was just a child but I was having to dial 999 when mum became so violently ill she was delirious.

“It put huge pressure on the family because our lovely mum, who had been so strong and active, lost her confidence and energy. Most of the time she was too tired to even sit and eat with us. What made it worse was we knew that the next stage of the illness was kidney failure, so it was like a timebomb ticking away.”

Her mother, Elaine, had developed Focal Segmental Glomerulosclerosis (FSGS), which means the kidneys can no longer filter blood, characterised by widespread scarring of the organs.

No one knows what causes the condition and it may have been dormant in Elaine since birth, and was diagnosed by a blood test only when she went to the doctor complaining of tiredness and swollen legs in 2001.

Because of the nature of FSGS, finding a donor is incredibly difficult, too. As the disease has an auto-immune element, she cannot receive a transplant from a relative. Her body is already primed to reject tissue that is genetically similar, increasing the risk that the transplant will fail.

Two years after her diagnosis, the inevitable happened: Elaine’s kidneys failed, she was put on dialysis – and family life became even more restricted.

“Once, when I was at university trying to write my dissertation, Mum developed a blood clot that stretched from her hand right up to her armpit. She was rushed to hospital, and I rushed to be by her side. The worst bit was watching her so ill and unhappy,” says Stephanie.

Listening to her daughter speak, in the neat sitting room of the family’s cottage in the Berkshire village of Binfield, Elaine, 54, is visibly moved.

Being unable to mother the children she so adores – she also has a son, James, 27 – is clearly heartbreaking. “I don’t like to think of my children’s lives being impeded by mine. I want to be doing things for them; not the other way around,” she says, her voice faltering. “When I imagined this stage of my life, I wanted my kids to be proud of me and for me to be holding down a good job, providing for them.

“The disease took away my future and my children lost the mother they had had. Every time I went to hospital, the doctors would show me how much my kidneys had deteriorated, and I was consumed by my own mortality.”

Elaine’s illness has become her life. She works part-time as a receptionist but is in constant pain and spends 20 hours a week hooked up to a dialysis machine to keep her alive.

Without a transplant, Elaine’s life will be cut short by the disease. There are around 6,000 people on the transplant list in Britain, with an average waiting time of three years – longer if the patient’s tissue type, blood type or illness is rare. In Elaine’s case, the odds of finding a match are less than one in 10,000.

A few months ago, as the family began to lose hope, Stephanie took decisive action, by launching a Facebook page to find her mother a kidney. “I was frustrated by not being able to control anything and a friend said she had seen similar things done in the US, so why didn’t I try it?” explains Stephanie, who works as a sales executive. “Overnight we had 300 likes and it has just grown from there.

“Already two people have been tested to see if they are a possible match, which sadly they weren’t, but the response has been unbelievable. One person offered to drive down from Manchester to be tested and a mother who is 33 weeks’ pregnant got in touch because she had lost an uncle to kidney failure. We haven’t been able to respond to all the emails and offers of help.”

Elaine wept when she heard what her daughter had done, and says she finds Stephanie’s strength “inspirational”. “It is a huge thing to ask someone to do and I feel really humbled. If just one person, who hadn’t thought of it before, signs up to the living donor register, that would be a huge achievement.”

A spokesman for the Human Tissues Authority, which regulates living donor transplants in the UK, last year issued guidelines for anyone launching an online appeal for donors, reminding them that it is illegal to offer payment. “At the moment, there haven’t been any cases of people being matched through social media – but that’s not to say it will never happen,” a spokesman said yesterday.

Across the Atlantic, there are thousands of sites similar to Stephanie’s – and many have had extraordinary results. Hannah Craig, a 21-year-old from Tampa Bay in Florida, who suffers from an auto‑immune disorder, found a kidney donor just a week after her cousin put an appeal on Facebook in 2012. The operation was successful, and she and the donor – someone who was moved by her story – are now firm friends.

Jeff Kurze, 35 from Michigan, who suffered from kidney failure, found his donor online, too. In 2011, his wife posted an appeal on the internet – and a stranger came forward to offer his organ.

In Cardiff last month, eight-year-old Hollie Clark, who has a rare bone marrow syndrome, found a donor three months after her parents’ online appeal went viral. Their plea for help led to a 2,580 per cent increase in the number of people in Wales joining the Anthony Nolan register. She is due to have a transplant this month.

The Reynoldses are inspired by others who have been down the same route, and touched that so many people from around the world have offered to help them. But what if no one suitable comes forward? “I don’t really like to think about that,” says Stephanie, her voice dropping to a whisper. “She’d have to just stay on dialysis until her body can’t cope any more.

“The average life expectancy of someone in her position is 10 years. I know that because I looked it up when I was 16 and started thinking, 'Right, I have to get married and have kids before I’m 26 so my mum can be there for it…”

Tears fill her eyes and her sentence trails off. Elaine puts her arm around her daughter and speaks for them both. “I find it hard to put into words what the operation would mean to me. I just want to do ordinary things, like going to work and coming home and cooking dinner and being a proper family again. Whether I find a donor or not, the most important thing is that we are raising awareness.”

Stephanie nods. “Seeing how many people care through this Facebook page has been such a boost for to us both. Already I feel like I have got my old mum back. Anything else would be just brilliant.”